Average Error: 10.5 → 0.0
Time: 2.0s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \frac{x}{z} \cdot \left(1 - y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \frac{x}{z} \cdot \left(1 - y\right)
double f(double x, double y, double z) {
        double r767184 = x;
        double r767185 = y;
        double r767186 = z;
        double r767187 = r767186 - r767184;
        double r767188 = r767185 * r767187;
        double r767189 = r767184 + r767188;
        double r767190 = r767189 / r767186;
        return r767190;
}
↓
double f(double x, double y, double z) {
        double r767191 = y;
        double r767192 = x;
        double r767193 = z;
        double r767194 = r767192 / r767193;
        double r767195 = 1.0;
        double r767196 = r767195 - r767191;
        double r767197 = r767194 * r767196;
        double r767198 = r767191 + r767197;
        return r767198;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.5
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.5

    \[\frac{x + y \cdot \left(z - x\right)}{z}\]

  2. Taylor expanded around 0 3.6

    \[\leadsto \color{blue}{\left(\frac{x}{z} + y\right) - \frac{x \cdot y}{z}}\]

  3. Taylor expanded around 0 3.6

    \[\leadsto \left(\frac{x}{z} + y\right) - \color{blue}{\frac{x \cdot y}{z}}\]

  4. Simplified0.0

    \[\leadsto \left(\frac{x}{z} + y\right) - \color{blue}{\frac{x}{z} \cdot y}\]

  5. Taylor expanded around 0 3.6

    \[\leadsto \color{blue}{\left(\frac{x}{z} + y\right) - \frac{x \cdot y}{z}}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{y + \frac{x}{z} \cdot \left(1 - y\right)}\]

  7. Final simplification0.0

    \[\leadsto y + \frac{x}{z} \cdot \left(1 - y\right)\]

Reproduce

herbie shell --seed 2020002 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))